Project Employees I: Employee Hierarchy Analysis

You are tasked with analyzing a company's employee structure to identify direct and indirect reporting relationships. This is crucial for understanding organizational flow, managing approvals, and performing impact assessments. You will build a system to process an employee hierarchy and determine who reports to whom, directly or indirectly.

Problem Description

The goal is to process a list of employee relationships and determine the reporting manager for each employee. An employee's manager can be their direct supervisor or a supervisor higher up in the hierarchy. You need to return a mapping where each employee is associated with their ultimate reporting manager.

Key Requirements:

1. Process Employee Relationships: You will be given a dataset representing who reports to whom. This data will be in the form of pairs, where the first element is the employee and the second element is their direct manager.
2. Determine Ultimate Manager: For every employee, identify their ultimate reporting manager. This is the highest-level manager in their reporting chain. If an employee has no manager (e.g., the CEO), they are their own ultimate manager.
3. Handle Circular Dependencies (Optional but good to consider): While ideally hierarchies are acyclic, consider how your solution might behave or what it should report if a circular dependency is present (e.g., A reports to B, and B reports to A). For this challenge, assume valid, acyclic hierarchies unless otherwise specified in constraints.
4. Output Format: The output should be a collection (e.g., a map or dictionary) where each employee's identifier is a key, and their ultimate manager's identifier is the corresponding value.

Expected Behavior:

• If employee X reports directly to manager Y, and manager Y reports directly to CEO Z, then X's ultimate manager is Z.
• If an employee is at the top of the hierarchy (i.e., has no manager listed), their ultimate manager is themselves.

Edge Cases to Consider:

• Employees who are at the top of the hierarchy.
• A flat hierarchy where everyone reports directly to a single manager.
• A very deep hierarchy.
• An empty input list of relationships.

Examples

Example 1:

Input:
Relationships: [("Alice", "Bob"), ("Bob", "Charlie"), ("David", "Bob"), ("Eve", "Charlie"), ("Charlie", "Frank")]

Output:
{
  "Alice": "Frank",
  "Bob": "Frank",
  "Charlie": "Frank",
  "David": "Frank",
  "Eve": "Frank"
}

Explanation:

• Alice reports to Bob, Bob reports to Charlie, Charlie reports to Frank. So, Alice's ultimate manager is Frank.
• Bob reports to Charlie, Charlie reports to Frank. Bob's ultimate manager is Frank.
• Charlie reports to Frank. Charlie's ultimate manager is Frank.
• David reports to Bob, Bob reports to Charlie, Charlie reports to Frank. David's ultimate manager is Frank.
• Eve reports to Charlie, Charlie reports to Frank. Eve's ultimate manager is Frank.
• Frank has no manager listed, so Frank is his own ultimate manager. However, since Frank is the ultimate manager for all others, he appears as the value.

Example 2:

Input:
Relationships: [("Alice", "CEO"), ("Bob", "Alice"), ("Charlie", "Alice")]

Output:
{
  "Alice": "CEO",
  "Bob": "CEO",
  "Charlie": "CEO",
  "CEO": "CEO"
}

Explanation:

• Alice reports to CEO. Alice's ultimate manager is CEO.
• Bob reports to Alice, Alice reports to CEO. Bob's ultimate manager is CEO.
• Charlie reports to Alice, Alice reports to CEO. Charlie's ultimate manager is CEO.
• CEO is at the top, so their ultimate manager is CEO.

Example 3:

Input:
Relationships: [] (Empty list)

Output:
{}

Explanation: An empty list of relationships results in an empty output mapping.

Constraints

• The number of employees can range from 0 to 1000.
• Employee identifiers are strings and can contain alphanumeric characters.
• The input Relationships will be a list of pairs (tuples or arrays), where each pair (employee, manager) indicates employee reports to manager.
• It is guaranteed that the hierarchy is acyclic (no employee directly or indirectly reports to themselves).
• A valid employee identifier will always be present as either an employee or a manager in at least one relationship, or be the ultimate manager of someone.
• The performance of your solution should be efficient, aiming for a time complexity that scales well with the number of employees and relationships, ideally close to linear time with respect to the total number of people involved.

Notes

• You might need a way to store the direct reporting structure first, and then traverse it to find the ultimate manager.
• Consider using recursion or iteration with a mechanism to avoid redundant computations for employees whose ultimate manager has already been determined.
• The problem statement implies that if an employee is mentioned as a manager but not as an employee in any relationship, they are at the top of a reporting chain.